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quantum algorithm for Solving the Continuous Hidden Symmetry Subgroup Problem

IEEE ACCESS 2021年 9卷 93248-93254页

作者： Bae, Eunok Lee, Soojoon Kyung Hee Univ Dept Math Seoul 02447 South Korea Kyung Hee Univ Res Inst Basic Sci Seoul 02447 South Korea

quantum computers are expected to be able to outperform classical computers. In fact, some computational problems such as integer factorization can be solved on quantum computers substantially faster than classical computers. Interestingly, these problems can be cast in a framework of the hidden symmetry subgroup problem. However, only a few of quantum algorithms for effciently solving this problem have been known, and the approaches used in all previous results can be applied to particular groups with specific group actions. In this paper, we introduce new technique for solving the hidden symmetry subgroup problem which can be applicable for any groups and any group actions with a certain condition. In addition, we define the continuous hidden symmetry subgroup problem on a group by employing a continuous oracle function, and prove that if the group is a metric space and the group action satisfies some condition, then the continuous hidden symmetry subgroup problem can be efficiently reduced to the continuous hidden subgroup problem. In particular, we show that there exists an efficient quantum algorithm to solve the continuous hidden symmetry subgroup problem on R-n, while it has not yet been shown that the original hidden symmetry subgroup problem on R-n can be efficiently solved by a quantum computer.

关键词： quantum algorithm continuous hidden symmetry subgroup problem hidden symmetry subgroup problem

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quantum algorithm for Position Weight Matrix Matching

IEEE TRANSACTIONS ON QUANTUM ENGINEERING

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IEEE TRANSACTIONS ON quantum ENGINEERING 2023年第1期4卷 1页

作者： Miyamoto, Koichi Yamamoto, Naoki Sakakibara, Yasubumi Osaka Univ Ctr Quantum Informat & Quantum Biol Toyonaka 5600043 Japan Keio Univ Dept Appl Phys & Physico Informat Yokohama 2238521 Japan Keio Univ Quantum Comp Ctr Yokohama 2238521 Japan Keio Univ Dept Biosci & Informat Yokohama 2238521 Japan

In this article, we propose two quantum algorithms for a problem in bioinformatics, position weight matrix (PWM) matching, which aims to find segments (sequence motifs) in a biological sequence, such as DNA and protein that have high scores defined by the PWM and are, thus, of informational importance related to biological function. The two proposed algorithms, the naive iteration method and the Monte-Carlo-based method, output matched segments, given the oracular accesses to the entries in the biological sequence and the PWM. The former uses quantum amplitude amplification (QAA) for sequence motif search, resulting in the query complexity scaling on the sequence length n, the sequence motif length m, and the number of the PWMs K as O(m root Kn), which means speedup over existing classical algorithms with respect to n and K. The latter also uses QAA and, further, quantum Monte Carlo integration for segment score calculation, instead of iteratively operating quantum circuits for arithmetic in the naive iteration method;then, it provides the additional speedup with respect to m in some situation. As a drawback, these algorithms use quantum random access memories, and their initialization takes O(n) time. Nevertheless, our algorithms keep the advantage especially when we search matches in a sequence for many PWMs in parallel

关键词： Pulse width modulation quantum algorithm Complexity theory DNA Proteins Biology Bioinformatics position weight matrix (PWM) matching quantum algorithm quantum amplitude amplification (QAA) quantum Monte Carlo integration (QMCI)

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quantum algorithm for sat problem and quantum mutual entropy

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REPORTS ON MATHEMATICAL PHYSICS 2005年第1期55卷 109-125页

作者： Ohya, M Tokyo Univ Sci Dept Informat Sci Noda Chiba 278 Japan

It is von Neumann who opened the window for today's information epoch. He defined quantum entropy including Shannon's information more than 20 years ahead of Shannon, and he explained what computation means mathematically. In this paper I discuss two problems studied recently by me and my coworkers. One of them concerns a quantum algorithm in a generalized sense solving the SAT problem (one of NP complete problems) and another concerns quantum mutual entropy properly describing quantum communication processes.

关键词： quantum mutual entropy quantum algorithm

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quantum algorithm to find invariant linear structure of MD hash functions

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quantum INFORMATION PROCESSING 2015年第3期14卷 813-829页

作者： Wu, WanQing Zhang, HuanGuo Mao, ShaoWu Wang, HouZhen Wuhan Univ Comp Sch Wuhan 430072 Peoples R China

In this paper, we consider a special problem. "Given a function f : {0, 1}(n) -> {0, 1}(m). Suppose there exists a n-bit string alpha is an element of{0, 1}(n) subject to f (x circle plus alpha) = f (x) for for all(x) is an element of{0, 1}(n). We only know the Hamming weight W(alpha) = 1, and find this alpha." We present a quantum algorithm with "Oracle"to solve this problem. The successful probability of the quantum algorithm is (2(l) - 1/2(l))(n-1), and the time complexity of the quantum algorithm is O(log(n - 1)) for the given Hamming weight W(alpha) = 1. As an application, we present a quantum algorithm to decide whether there exists such an invariant linear structure of the MD hash function family as a kind of collision. Then, we provide some consumptions of the quantum algorithms using the time-space trade-off.

关键词： MD Hash functions Invariant linear structure quantum algorithm quantum network

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quantum algorithm for Poisson Equation with Inhomogeneous Media

Quantum Algorithm for Poisson Equation with Inhomogeneous Me...

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International Applied-Computational-Electromagnetics-Society Symposium - China (ACES)

作者： Dang, Xunwang Li, Liangsheng Yin, Hongcheng Liu, Yong-Qiang Sci & Technol Electromagnet Scattering Lab Beijing Peoples R China

ISBN: (纸本)9780996007894

quantum computer has attracted much attention from academy and industry due to the marvelous acceleration compared with classical computers. A quantum computing algorithm for Poisson equations with inhomogeneous media is presented here. The original equation is discretized with square grids and transformed into linear equations using finite difference method. Then the quantum algorithm for solving sparse matrix equations is applied to the discretized Poisson equation. The quantum algorithm can achieve O(logN) complexity. Numerical simulations verify the accuracy of such algorithm.

关键词： quantum algorithm Poisson equation finite difference method

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quantum algorithm for programmed cell death of Caenorhabditis elegans

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BIOCHEMICAL AND BIOPHYSICAL RESEARCH COMMUNICATIONS 2004年第3期321卷 515-516页

作者： Dong, KJ Qian, JX Hainan Med Coll Transgen Lab Haikou 571101 Peoples R China

During the development of Caenorhabditis elegans, through cell divisions, a total of exactly 1090 cells are generated, 131 of which undergo programmed cell death (PCD) to result in an adult organism comprising 959 cells. Of those 131, exactly 113 undergo PCD during embryogenesis. subdivided across the cell lineages in the following fashion: 98 for AB lineage;14 for MS lineage;and 1 for C lineage. Is there a law underlying these numbers, and if there is, what Could it be? Here we wish to show that the count of the cells undergoing PCD complies with the cipher laws related to the algorithms of Shor and of Grover. (C) 2004 Elsevier Inc. All rights reserved.

关键词： quantum algorithm programmed cell death Caenorhabditis elegans

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quantum algorithm for copula-based risk aggregation using orthogonal series density estimation 5

Quantum algorithm for copula-based risk aggregation using or...

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2024 International Conference on quantum Computing and Engineering

作者： Mori, Hitomi Miyamoto, Koichi Osaka Univ Grad Sch Engn Sci Toyonaka Osaka Japan Osaka Univ Ctr Quantum Informat & Quantum Biol Toyonaka Osaka Japan

ISBN: (纸本)9798331541378

quantum Monte Carlo integration (QMCI) provides a quadratic speed-up over its classical counterpart, and its applications have been investigated in various fields, including finance. This paper considers its application to risk aggregation, one of the most important numerical tasks in financial risk management. Risk aggregation combines several risk variables and quantifies the total amount of risk, taking into account the correlation among them. For this task, there exists a useful tool called copula, with which the joint distribution can be generated from marginal distributions with a flexible correlation structure. Classically, the copula-based method utilizes sampling of risk variables. However, this procedure is not directly applicable to the quantum setting, where sampled values are not stored as classical data, and thus no efficient quantum algorithm is known. In this paper, we introduce a quantum algorithm for copula-based risk aggregation that is compatible with QMCI. In our algorithm, we first estimate each marginal distribution as a series of orthogonal functions, where the coefficients can be calculated with QMCI. Then, by plugging the marginal distributions into the copula and obtaining the joint distribution, we estimate risk measures using QMCI again. With this algorithm, nearly quadratic quantum speed-up can be obtained for sufficiently smooth marginal distributions.

关键词： quantum algorithm quantum Monte Carlo integration Finance Risk aggregation

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quantum algorithm for Triangle Finding in Sparse Graphs 26th

Quantum Algorithm for Triangle Finding in Sparse Graphs

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26th International Symposium on algorithms and Computation (ISAAC)

作者： Le Gall, Francois Nakajima, Shogo Univ Tokyo Dept Comp Sci Grad Sch Informat Sci & Technol Tokyo Japan

ISBN: (纸本)9783662489710;9783662489703

This paper presents a quantum algorithm for triangle finding over sparse graphs that improves over the previous best quantum algorithm for this task by Buhrman et al. (SIAM J Comput 34(6):1324-1330, 2005). Our algorithm is based on the recent (O) over tilde (n(5/4))-query algorithm given by Le Gall (Proceedings of the 55th IEEE annual symposium on foundations of computer science, pp 216-225, 2014) for triangle finding over dense graphs (here n denotes the number of vertices in the graph). We show in particular that triangle finding can be solved with O(n(5/4-epsilon)) queries for some constant epsilon > 0 whenever the graph has at most O(n(2-c))edges for some constant c > 0.

关键词： quantum algorithm quantum walk Triangle finding

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quantum algorithm for Finding Impossible Differentials and Zero-Correlation Linear Hulls of Symmetric Ciphers 28th

Quantum Algorithm for Finding Impossible Differentials and Z...

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28th Australasian Conference on Information Security and Privacy (ACISP)

作者： Chen, Huiqin Li, Yongqiang Abla, Parhat Li, Zhiran Jiao, Lin Wang, Mingsheng Chinese Acad Sci Inst Informat Engn Beijing Peoples R China South China Normal Univ Sch Software Guangzhou Peoples R China State Key Lab Cryptol Beijing Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing Peoples R China

ISBN: (纸本)9783031354854;9783031354861

In this paper, we present quantum algorithms for finding impossible differentials and zero-correlation linear hulls, which are distinguishers for the two powerful attacks against symmetric ciphers of impossible differential attack and zero-correlation linear attack. Compared to classical methods, the proposed quantum algorithms possess many advantages. Firstly, our quantum algorithm for finding impossible differentials obtains the input and output differences by solving linear equation systems instead of searching in a limited space;Secondly, our quantum algorithm for zero-correlation linear hulls can investigate the key schedule's effect;Thirdly, the only computation cost of our algorithms is solving linear equation systems, and the size of the systems is not increasing as the round number increases. The core idea of our method is to use the Berstein-Vazirani algorithm to find 1-linear structures of Boolean functions. We check the validity of the proposed quantum algorithm with the SIMON block cipher family and RC5 block cipher. We show that the proposed algorithms can discover some 11-round, 12-round, 13-round, 16-round, and 19-round impossible differentials and zero-correlation linear hulls of SIMON cipher when considering the key schedules and 2.5-round impossible differential of RC5 when considering the round subkeys.

关键词： quantum algorithm Berstein-Vazirani algorithm Linear structure Impossible differential Zero-correlation linear hull

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quantum algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs 1

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18th International Conference on Unconventional Computation and Natural Computation (UCNC)

作者： Khadiev, Kamil Safina, Liliya Smart Quantum Technol Ltd Kazan Russia Kazan Fed Univ Kazan Russia

ISBN: (数字)9783030193119

ISBN: (纸本)9783030193119;9783030193102

In this paper, we present a quantum algorithm for dynamic programming approach for problems on directed acyclic graphs (DAGs). The running time of the algorithm is O(root(n) over cap mlog (n) over cap), and the running time of the best known deterministic algorithm is O(n + m), where n is the number of vertices, (n) over cap is the number of vertices with at least one outgoing edge;m is the number of edges. We show that we can solve problems that use OR, AND, NAND, MAX and MIN functions as the main transition steps. The approach is useful for a couple of problems. One of them is computing a Boolean formula that is represented by Zhegalkin polynomial, a Boolean circuit with shared input and non-constant depth evaluating. Another two are the single source longest paths search for weighted DAGs and the diameter search problem for unweighted DAGs.

关键词： quantum computation quantum models quantum algorithm Query model Graph Dynamic programming DAG Boolean formula Zhegalkin polynomial DNF AND-OR-NOT formula NAND Computational complexity Classical vs. quantum Boolean formula evaluation

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